The angle of elevation from a soccer ball on the ground to the top of the goal is 34. if the goal is 8 ft tall, what is the distance from the ball to the goal?

You can use the Pythagorean Theorem. Which is a^2 + b^2 = c^2.

So now to plug in the equation.

In your case a is 8 and c is 34. So now we need to solve for b.

8 squared is equal to 64.
34 squared is equal to 1156.

Now to plug things in.

64 + b^2 = 1156

Now subtract 64 from 1156.

That equals 1092.
The equation is now

b^2 = 1092

Now do the square root of 1092.

But since the square root is an irrational number you can just write b = 1092 ( but put a square root with 1092)